Orbital stability for periodic standing waves of the Klein-Gordon-Zakharov system and the beam equation

DOI10.1007/s00033-012-0228-6zbMath1270.35082arXiv1012.3065OpenAlexW2085720936MaRDI QIDQ353376

Milena Stanislavova, Atanas G. Stefanov, Sevdzhan A. Hakkaev

Publication date: 12 July 2013

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3065

zbMATH Keywords

orbital stabilityperiodic traveling wavesbeam equationGrillakis-Shatah-Strauss type conditionKlein-Gordon-Zakharovlow regularity initial data

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Traveling wave solutions (35C07) Second-order hyperbolic systems (35L51) Second-order semilinear hyperbolic equations (35L71)

Related Items (4)

On the Stability of the Periodic Waves for the Benney System ⋮ Linear stability of periodic standing waves of the KGZ system ⋮ Orbital stability of solitary waves of the coupled Klein-Gordon-Zakharov equations ⋮ Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation

Cites Work

• Instability of standing waves for Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions
• Stability theory of solitary waves in the presence of symmetry. II
• Stability theory of solitary waves in the presence of symmetry. I
• Well-posedness in energy space for the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions
• On the Cauchy problem for the Zakharov system
• Stability and instability of fourth-order solitary waves
• Orbital stability of solitary waves for the Klein-Gordon-Zakharov equations
• Normal form and global solutions for the Klein-Gordon-Zakharov equations
• Conditional stability theorem for the one dimensional Klein-Gordon equation
• Uniqueness of Solutions for Zakharov Systems
• Travelling Waves in a Suspension Bridge
• Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System
• Non-Uniform Dependence for the Periodic CH Equation
• Strong Instability of Standing Waves for the Nonlinear Klein–Gordon Equation and the Klein–Gordon–Zakharov System

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